Information on Result #675402
Linear OA(3246, 6631, F3, 42) (dual of [6631, 6385, 43]-code), using construction X applied to C([0,21]) ⊂ C([0,16]) based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(321, 69, F3, 8) (dual of [69, 48, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3247, 6632, F3, 42) (dual of [6632, 6385, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3246, 6555, F3, 2, 42) (dual of [(6555, 2), 12864, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3246, 6555, F3, 3, 42) (dual of [(6555, 3), 19419, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3246, 6555, F3, 4, 42) (dual of [(6555, 4), 25974, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(3246, 6555, F3, 5, 42) (dual of [(6555, 5), 32529, 43]-NRT-code) | [i] | ||
| 6 | Digital (204, 246, 6555)-net over F3 | [i] | ||